The propagating crack problems under dynamic antiplane mode in orthotropic material is studied in this paper. To analyze the dynamic fracture problems by theoretical method or experimental method in orthotropic material, it is important to know the dynamic stress intensity factor in the vicinity of crack tip. Therefore the dynamic stress field and dynamic displacement field with dynamic stress intensity factor of orthotropic material in mode III were derived. When the crack propagation speed approachs to zero, the dynamic stress components and dynamic displacement components derived in this paper are identical to the those of static state. In addition, the relationships between dynamic stress intensity factor and dynamic energy release rate are determined by using the concept of crack closure energy with the dynamic stresses and dynamic displacements derived in this paper. Finally, the characteristics of crack propagation are studied with the properties of orthotropic material and crack speed. The variation of angle .alpha. between fiber direction and crack propagating direction and crack propagation speed fairly effect on stress component and displacement component in crack tip. The influence of crack propagation speed on the speed on the stress and displacement is greater in the case of .alpha.=90.deg. than in the case of .alpha.=0.deg. and the faster the crack propagation speed, the greater the stress value and displacement value.